The y-intercept occurs when $x = 0$. Let's analyze the transformation of the function $g(x)$ into $g\left(\frac{1}{2}x\right)$.

1. We know that $g(x)$ has a y-intercept at $(0, 5)$, meaning $g(0) = 5$.
2. The transformed function $g\left(\frac{1}{2}x\right)$ still needs the value at $x = 0$ to find the y-intercept: $g\left(\frac{1}{2}(0)\right) = g(0) = 5.$

Since $g(0) = 5$ for both $g(x)$ and $g\left(\frac{1}{2}x\right)$, the y-intercept of $g\left(\frac{1}{2}x\right)$ is still $(0, 5)$.

Thus, the correct answer is:

b. (0, 5)

Would you like more details or have any further questions?

Related Questions:

1. What happens to the graph of a function when you stretch it horizontally?
2. How does a vertical stretch affect the y-intercept of a function?
3. What is the difference between horizontal and vertical transformations in functions?
4. How can we find the x-intercept of $g\left(\frac{1}{2}x\right)$ if it exists?
5. How does the slope of a linear function change with horizontal stretching?

Tip: Horizontal stretches/compressions affect the x-values, but they do not change the y-intercept unless there's a vertical shift.